If x = 2/3y and y = 18, what is the value of 2x − 3 ? A) 21 B) 15 C) 12 D) 10
Our end goal is to figure out what 2x - 3 is equal to so that we can answer the question. In order to do this, we have to do 2 steps in this question. First, we need to figure out what x is equal to. We notice that there are two variables in this question: x and y. It is always nice to get rid of as many variables as we can, and in this question, they tell us that y is equal to 18. So we can substitute y into the equation as follows: x = 2/3y x = 2/3(18) x = 12 Now that we know that x is equal to, we can move on to the second part of the question: plugging x = 12 into the 2x-3 equation as follows: 2x - 3 = ? 2(12) - 3 = ? 24 - 3 = ? 24 - 3 = 21 Thus our answer choice would be A.
A hockey puck of mass 0.16 kg is slapped so that its velocity is 50 m/sec. It slides 40 meters across the ice before coming to rest. How much work is done by friction on the puck? A. 4 J B. -60 J C. -200 J D. -340 J
The work-energy principle states that the work done on an object is equal to the change in the kinetic energy of that object. In this example, the work done on the puck is equal to the change in the kinetic energy of the puck. As a reminder, the formula for kinetic energy is: ½mv^2 The change in kinetic energy of the puck is: Final kinetic energy minus initial kinetic energy Using the formula for kinetic energy, this would be: ½(mass)(final velocity)^2 - ½(mass)(initial velocity)^2 = ½(0.16 kg)(0 m/sec)^2 - ½(0.16 kg)(50 m/sec)^2 = 0 - 200 kg*m/sec = -200 kg*m/sec = -200 J Note that kg*m/sec is equivalent to Joules Thus, our answer choice would be C.
A car averages 27 miles per gallon. If gas costs $4.04 per gallon, which of the following is closest to how much the gas would cost for this car to travel 2,727 typical miles? A. $44.44 B. $109.08 C. $118.80 D. $408.04 E. $444.40
There are 2 parts to this question. First, we see that the gas costs $4.04 per gallon, but we do not yet know how many gallons the car needs to travel 2,727 miles. However, the question stem tells us that the car averages 27 miles per gallon, so we can do the following math to convert from miles to gallons: 2,727 miles x 1 gallon 2,727 ------------- = --------- = 101 gallons 27 miles 27 Now for the second part. We now know that the car will use 101 gallons for the trip. Knowing that the gas costs $4.04 per gallon, we can do the following math: 101 gallons x $4.04 $408.04 ----------- = ------------- = $408.04 1 gallon 1 The final answer is $408.04. Answer D. *As an extra point, note how in the first math example, the units for "miles" both cancel out, leaving you with only gallons as the unit at the end (101 gallons). For the second math example, the units for "gallons" cancel out, leaving you with only dollars as the unit ($408.04).